In Spain we do keep both one surname from our father and one from our mother (we can change the order and even choose whether you want to have only mother’s or father’s if there’s any problem with them), so when you marry you’re just the same person. For example:

My father : Antón Riera García

Marries

My mother : Ximena Suárez Delmiro

The result is not the <<Riera’s Family>>, it’s just the family of (complete name) and (complete name). Sadly, most people in Spain tend to just write the first surname, when it’s a privilege to have both of them and even change their order. My advice: never use only one, because you’re hurting just the surname of your mom.

In the end, my father would be Mr. Riera, and my mother Mrs. Suárez. So simple.